A224934 Primes p for which there exists no prime q, different from p, such that p+q-1 is the next prime after p.

2, 3, 89, 113, 293, 317, 359, 389, 401, 449, 479, 491, 683, 701, 719, 743, 761, 773, 839, 863, 887, 911, 929, 953, 983, 1109, 1163, 1193, 1327, 1373, 1409, 1439, 1523, 1559, 1571, 1583, 1637, 1669, 1733, 1823, 1847, 1979, 2003, 2039, 2153, 2179, 2213, 2243

Offset

1,1

Comments

If we relax the restriction on q, where q is different from p, 2 and 3 fail to be members of this sequence.

Primes p = prime(k) for which A076368(k+1) = p or A076368(k+1) is composite. - Robert Israel, Nov 21 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

89 is in the list because there exists no prime q such that 89 + q - 1 = 97.

Maple

N:= 10^4: # to get all terms p for which the next prime <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
G:= P[2..-1]-P[1..-2]:
P[select(t -> G[t]=P[t]-1 or not isprime(G[t]+1), [$1..nops(G)])]; # Robert Israel, Nov 21 2016

Mathematica

t = {}; Do[p = Prime[n]; If[FreeQ[Table[k = p + Prime[i] - 1, {i, n - 1}], Prime[n + 1]], AppendTo[t, p]], {n, 335}]; t

Crossrefs

Cf. A076368, A224748.

Sequence in context: A246121 A356798 A356788 * A299691 A042901 A356796

Adjacent sequences: A224931 A224932 A224933 * A224935 A224936 A224937

Keyword

nonn

Author

Jayanta Basu, Apr 20 2013

Status

approved